Mac – .putty/randomseed in home folder

Bash has special provisions in its source code to source ~/.bashrc when it's invoked by rshd or sshd. It's a compilation option, which given your experience seems not to be turned on under OSX.

If you're logging in with a key, you can (ab)use the command= option in the ~/.ssh/authorized_keys file. A key with a command option is good only for running the specified command; but the command in the authorized_keys file runs with the environment variable SSH_ORIGINAL_COMMAND set to the command the user specified (empty for interactive sessions). So you can use something like this in ~/.ssh/authorized_keys (of course, it won't apply if you don't use this key to authenticate):

command=". ~/.profile;
         if [ -n \"$SSH_ORIGINAL_COMMAND\" ]; then
           eval \"$SSH_ORIGINAL_COMMAND\";
         else exec \"$SHELL\"; fi" ssh-rsa …

Note that I put line breaks above for legibility, but this actually needs to be all on one line.

How can I set environment variables for a remote rsync process? may have other helpful suggestions.

It's almost certainly harmless. If you select a file on the desktop (even unintentionally) and press enter and then type ok - that would explain the naming.

I would open the terminal app (/Applications/Utilities) and type file and then drag the questionable file into the window and press enter.

That will look at the file contents and give you a hint about what it might contain. Spotlight information could help find other files around the same time, but I'd start with the file tool and get more information or just delete the file named OK - especially if you have a backup where you could get back what you lost if you find out later it was an image or document you needed.